Reduce to lowest terms: $- \dfrac{8}{5} \div \dfrac{2}{3} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{2}{3}$ is $ \dfrac{3}{2}$ Therefore: $ - \dfrac{8}{5} \div \dfrac{2}{3} = - \dfrac{8}{5} \times \dfrac{3}{2} $ $ \phantom{- \dfrac{8}{5} \times \dfrac{3}{2}} = \dfrac{-8 \times 3}{5 \times 2} $ $ \phantom{- \dfrac{8}{5} \times \dfrac{3}{2}} = \dfrac{-24}{10} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{-24}{10} = \dfrac{-24 \div 2}{10 \div 2} = -\dfrac{12}{5} $